vipulgoyal wrote:If x and y are positive integers, is y divisible by 3?
(1) Y=2x^3+9x^2-5x.
(1) x is an odd number.
A
Statement 1: y=2x³+9x²-5x
y = x(2x² + 9x - 5)
y = x(2x-1)(x+5).
If x=1, then y = x(2x-1)(x+5) = 1*1*
6.
If x=2, then y = x(2x-1)(x+5) = 2*
3*7.
If x=3, then y = x(2x-1)(x+5) =
3*5*8.
If x=4, then y = x(2x-1)(x+5) = 4*7*
9.
If x=5, then y = x(2x-1)(x+5) = 5*
9*10.
If x=6, then y = x(2x-1)(x+5) =
6*11*11.
Note the diagonal pattern in red.
The pattern indicates that one of y's factors will always be a multiple of 3, with the result that y itself will always be a multiple of 3.
SUFFICIENT.
Statement 2: x is odd
No information about y.
INSUFFICIENT.
The correct answer is
A.
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